Find the domain of the real valued function of real variable:

(iii) \[f\left( x \right) = \sqrt{9 - x^2}\]

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#### Solution

(iii) Given:

\[f\left( x \right) = \sqrt{9 - x^2}\]

We observe that

9 -

⇒

⇒ (

⇒-3 ≤

Hence, domain (

*f*(*x*) is defined for all satisfying9 -

*x*^{2}≥ 0 .⇒

*x*^{2}-9 ≤ 0⇒ (

*x*+ 3)(*x*-3) ≤ 0⇒-3 ≤

*x*≤ 3*x*∈ [ -3, 3]Hence, domain (

*f*) = [-3, 3]Concept: Cartesian Product of Sets

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